Symbol rotation as dynamic essential to engaging with value-inversion

Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity (Part #12)

---

[Parts: First | Prev | All] [Links: To-K | From-K | From-Kx | Refs ]

---

Cognitive "resonance hybrids"? Assumptions regarding attribution of logical connectives and cognitive implications to sets of vertices, rather than sets of edges or faces, can be usefully challenged. Of particular concern is the capacity to comprehend the coherence of complex sets -- and to render them widely communicable. To this consideration might be added issues relating to the aesthetics of enabling symmetry as constituting a strange attractor of a particular kind -- by which any such model is rendered "interesting" rather than "confusing".

It is in this sense that it could be argued that the attribution to the 3-fold option of vertices, edges or faces could be explored in terms of alternation. This offers the implication that mappings could be based on a set of complementary models -- recalling the many distinctive projections through which the globe is mapped. Given the biomimetic inspiration of double-stranded DNA for the argument above, there is a case for recalling that the structure of the "benzene molecule" -- most fundamental to organic life -- is understood in terms of the dynamics of a resonance hybrid (of which there are many depictions, star-like and otherwise, notably inspired by August Kekulé).

Ouroboros benzene molecule as envisaged by Kekulé (from Wikipedia)	Cognitive resonance between modes of attribution to polyhedra (suggestive schematic)

Negative curvature? The case for topological complexification in the quest for more fundamental order can be made otherwise in terms of the significance accorded by astrophysicists to recognition of negative curvature and its implications for understanding the shape of the universe, as discussed separately (Eliciting a Universe of Meaning -- within a global information society of fragmenting knowledge and relationships, 2013). Recent research by Stephen Hawking and colleagues (Accelerated Expansion from Negative Lambda, 2012) has shown that the universe may have the same surreal geometry as some of art's most mind-boggling images (Lisa Grossman, Hawking's 'Escher-verse' could be theory of everything, New Scientist, 9 June 2012). This offers a way of reconciling the geometric demands of string theory, a still-hypothetical "theory of everything", with the universe as observed -- through a negatively-curved Escher-like geometry (essentially a hyperbolic space).

The insight relies on a mathematical twist previously considered impossible, namely the use of a negative cosmological constant rather than a positive one. The new approach provides a description of "all the possible universes that could have been -- including ones in which the solar system never formed, or in which life might have evolved quite differently". Making conventional use of a positive cosmological constant, it had proven impossible to describe universes that were "anything more than clunky approximations to reality". A plethora of universes have now been generated from wave functions with negative cosmological constants.

Arguably, whether discovered by artificial intelligence or otherwise, analogous topological breakthroughs may have significance for connectivity in the ways of knowing, as argued separately in relation to deprecated symbol systems (Engaging with Hyperreality through Demonique and Angelique? Mnemonic clues to global governance from mathematical theology and hyperbolic tessellation, 2016; Quest for a "universal constant" of globalization? Questionable insights for the future from physics, 2010). Might viable global governance require some analogue to negative curvature to render global order coherent?

Rotation of "existential" perspective? As noted above, considerable controversy is engendered in society by the inversion of some symbols (as with any cross or pentagon), or between left and right-facing (as in the case of the swastika). This can be variously explored (Unquestioned Bias in Governance from Direction of Reading? Political implications of reading from left-to-right, right-to-left, or top-down, 2016; Reversing the Anthem of Europe to Signal Distress: transcending crises of governance via reverse music and reverse speech? 2016).

It is significant that the attributions by logicians to polyhedra are indifferent as abstractions to what is implied by such inversion -- as understood in popular culture and in the depiction of symbols on flags (for example). This suggests that dimensions of existential significance are indeed "missing" from conventional academic understanding -- in accord with the above-mentioned argument of Terrence Deacon (2001, 2010).

The point may be explored otherwise in terms of the neglect in conventional models of any consideration of the role of some form of "corruption" -- notably in relation to the trilogy of academia / government / business in the Triple Helix model, for example. And yet the extent of such corruption (and its denial) is a matter of daily record in the media -- most notably at the highest level. In addition, just as the inversion of some symbols is associated with "evil", it is indeed the existence of "evil" which is frequently proclaimed and deprecated by the leaders of the world, notable for attributing that quality to their peers (Existence of evil as authoritatively claimed to be an overriding strategic concern, 2016; Which world leaders have (not) been labelled "evil"? 2015). The models above partially address this issue through the helical dynamics associated with a "cognitive wormhole" (perhaps usefully recognized as a "cognitive sinkhole") and reference to the process of enantiodromia highlighted by William Irwin Thompson (From Nation to Emanation: Planetary Culture and World Governance, 1982),

Encompassing the elusive: The question is then how the reality of such missing dimensions might be cognitively "encompassed", especially if they are "compactified" and "curled up" in a manner beyond the overriding preference for 3D frameworks (as for the rhombic dodecahedron), whatever necessity is perceived by logicians for the 4-dimensionality represented by a tesseract. This concern presumably includes the need to engage effectively with the reality of "fake news" and "spin", however much their truth may be called into question from a logical perspective.

It is therefore intriguing to note the efforts to depict the 4-dimensionality of a tesseract by animation, whilst at the same time begging the question of the potential relevance of hypercubes of higher dimensionality (penteract, hexeract, etc). The question is most clearly framed by the 6-level encoding of the I Ching hexagrams in contrast with the 4-level encoding required for the 16 Boolean connectives.

Arguably the 4-level encoding is completely adequate for encoding an essentially "mechanical" world view -- 3D entities in movement -- as framed by the tesseract. Higher orders of self-reference are effectively "designed out" -- notably in the light of the paradoxes they pose for physics in the observer-observed relationship. Given widespread institutional reference to strategic pillars (as noted above) as mechanical models, there is clearly a missing link in practice to experience of the implied value nexus -- although effectively aspiring to star-like configuration as "cognitive keystones" (Challenge of "soullessness" -- beyond the "pillar-ization of Europe", 2004; Paul Pardi, Has Science Become 'Soulless'? Philosophy News, 15 August 2013),

To the extent that such higher-order relationships call for 32 and 64 conditions -- beyond the 16 Boolean connectives -- it is interesting that these can be fruitfully mapped onto 3D polyhedral projections of the 4D polychoron -- the tesseract (in motion) -- in addition to the potential exception of the drilled truncated cube. However it is the cognitive significance of the process of projection which merits attention -- namely how 4-dimensionality (or higher) can be reduced to 3-dimensionality through truncation, rectification and other such processes.

It is in this sense that recognition of the necessary rotation of the corresponding star-like symbols enables a degree of 4-dimensionality to be encompassed and compehended in a 3-dimensional context. Hence the reference to eppur si muove.

Cognitive implication in the "missing dimensions": It is intriguing to note that the 16 Boolean connectives can be encoded by 4 levels of an I Ching hexagram -- a trigram plus one. The four values which can be taken by the last two levels -- the 5th and 6th -- then pose the question as to what they might signify, especially as modifiers of the preceding four (to encode a total of 64 "conditions of change"). The manner in which these are excluded from conventional thinking offers its own clue in that the last two levels four could be understood in terms of the tetralemma highlighted with respect to a necessary shift beyond formal logic by Kinhide Mushakoji (Scientific Revolution and Inter-paradigmatic Dialogue, United Nations University, 1979). The tetralemma is notably a feature of Indian logic as: affirmation, negation, both affirmation and negation, neither affirmation nor negation.

This pattern of comprehension might be usefully understood otherwise and more generally, perhaps such as to include western interest in enactivism and the psychosocial construction of reality (Peter L. Berger and Thomas Luckmann, The Social Construction of Reality, 1966), as separately discussed (En-minding the Extended Body: enactive engagement in conceptual shapeshifting and deep ecology, 2003). The pattern would then take the form of enaction (and the implied responsibility assumed), being enacted by (and the implied denial of responsibility), both conditions, and neither of them. This has the merit of engaging with currently problematic issues of radical choice, radical attribution of blame (identity politics), and plausible deniability -- all of which are beyond the scope of formal logic.

Another approach is through understanding use of any binary coding system to represent "filling up", namely with respect to any initial assumption as to whether broken and complete lines in the (hexagram, for example) appropriately represent 0 and 1 or, conversely, 1 and 0 (or the order in which a trigram might be read, top down or down up). The fundamental nature of this seemingly trivial assumption has been explored by Xavier Sallantin (L'épistémologie de l'arithmétique, Communication aux Seminaires internationaux d'épistemologie de l'Abbaye de Senanque, 1976). Sallantin exaplains this assumption in terms of how agreement is established when, depending on culture, "yes" may be denoted by a "nod" or a "shake" of the head (for example, by a referee tossing a coin for captains before a football match). The ambiguity is also recognized in the distinction between perceiving a glass as being "half-full" rather than "half-empty".

The question can be approached otherwise through the fine distinctions encoded and comprehensible through music -- potentially far beyond any limit at 32 or 64. In the various analyses by musicologist Ernest McLain (The Myth of Invariance: the origins of the gods, mathematics and music from the Rg Veda to Plato, 1976), his focus is on the distinctions made arising from patterns of multiples: 2^p x 3^q x 5^r and beyond. The cases of 64 (as 2⁶), 72 (as 2³ x 3²), or 108 (as 2² x 3²) are clearly only at the beginning of any such pattern, subject to comprehension constraints (Tonal patterns of Rg Veda poetry, 1984; Patterns of N-foldness: comparison of integrated multi-set concept schemes as forms of presentation, 1980; Comprehension of Numbers Challenging Global Civilization, 2014).

Any related reference to myth serves to emphasize that it is the patterns of myth -- and their associated symbols -- that tend to be especially memorable over extended periods of time, as catalysts for creative imagination for which appeals are made at this time (Engendering 2052 through Re-imagining the Present, 2012; Imagining the Real Challenge and Realizing the Imaginal Pathway of Sustainable Transformation, 2007).

Comprehension, insight and "catching the light"? In emphasizing the absence of self-reference in conventional logic it is interesting to note concern with the role of the observer in the orthographic projections -- by which Boolean connectives might be mapped, as argued above especially in the case of connectives of a higher dimensional order (Ian O. Angell, The Observer and the Orthographic Projection, 1990). This calls for clarification in relation to facet diagrams as indicated below.

Disambiguation of faceting

As noted in the Stella4D Manual, the faceting diagram of a polyhedron is reciprocal to the stellation diagram for its dual. There is a different faceting diagram for each different type of vertex of a polyhedron -- to be variously viewed (as with stellations). In their presentation they have a star-like resemblance to the orthographic projections -- both potentially having a striking aesthetic quality (as indicated above). Both have a resemblance to the gemstone faceting diagrams basic to the mechanical process of gemstone faceting: cutting surfaces on a piece of crystal in order to create beautiful gems. As diagrams, all three only imply an observer and their potential roles as a star-like symbol for that observer.

The process of developing a gem through cutting merits exploration as the elaboration of a symbol, given the major role that gems are widely held to have in embodying and expressing value -- whether on the crowns of royalty or on highly valued jewelry of various kinds. This is most notable in the case of the diamond -- a symbol of wisdom -- as may be speculatively explored (Current metaphoric applications of gemstones, 2002; Patterning Archetypal Templates of Emergent Order: implications of diamond faceting for enlightening dialogue, 2002). Gems can be readily recognized as the ultimate aesthetic expression of star-like symbols presented otherwise -- being especially attractive in that respect.

The fundamental point to be made in support of the argument above is the necessity of sequential eye movement to recognize the elegant symmetry of an individual gemstone from different perspectives, or that of orthographic projections and faceting diagrams -- of which a number may be relevant to any one polyhedron. Appreciation of symmetry may well require a rotary pattern of eye movement through which meaning is elicited and the pattern is held to be meaningful as a whole -- and to be valued as symbolic of a higher order. Gemstones are appreciated through moving them in order to "catch the light". Symbols can be understood as requiring movement to enable insight into the cognitive light of which they are indicative. Their use on national flags recalls the role of prayer flags fluttering in the wind.

Movement necessarily implies the dimension of time and a time-transcendent perspective, as discussed separately (Aesthetics of human understanding through embodiment, 2011). Mark Johnson, in particular has developed this understanding following his earlier work (The Meaning of the Body: aesthetics of human understanding, 2007; The Body in the Mind: the bodily basis of meaning, imagination, and reason, 1987). The argument is taken further with respect to embodiment of the mind in movement by Maxine Sheets-Johnstone (The Primacy of Movement, 2011). In contrast with the proccupations of logicians, the process is especially well illustrated by sports involving acrobatics and aerobatics.

If movement is primarily associated with 4-dimensionality, what is the role of self-referential insight in relation to the 5th and 6th dimension? Although the question may be framed as irrelevant to the conventions of "western" logic, it is appropriate to note the ever increasing insightful contributions of those of "eastern" cultures to the paradoxes of fundamental physics, as argued by Susantha Goonatilake, Toward a Global Science: mining civilizational knowledge, 1999). The traditional insights of those cultures may yet subsume the conventions of logic within a subtler framework of greater relevance to global governance (Enhancing the Quality of Knowing through Integration of East-West metaphors, 2000). However the cognitive frameworks of hypothetical extraterrestrials could well be an even greater challenge.

---

[Parts: First | Prev | All] [Links: To-K | From-K | From-Kx | Refs ]